Identify the null hypothesis, alternative hypothesis, test statistic, P-value, initial and final conclusion.
Test the claim that less than 54% of the people following a particular diet will experience increased energy. Of 100 randomly selected subjects who followed the diet, 60 noticed an increase in their energy level.
Use α = 0.05.
Identify the null hypothesis and alternative hypothesis.
["Ho: p=0.60 , H1: p > 0.60", "Ho: p=0.54 , H1: p ≠ 0.54", "Ho: p=0.45 , H1: p > 0.45", "Ho: μ=0.54 , H1: μ < 0.54", "Ho: μ=0.54 , H1: μ ≠ 0.54", "Ho: p=0.54 , H1: p < 0.54"]
Find the critical value(s):
["Z= -1.960", "t= -1.990", "Z= -1.645", "Z=1.645", "Z=1.960", "t=1.990"]
Find the test statistic.
["t=1.24", "Z=1.204", "t = 1.45", "Z= 1.240", "Z= -1.204"]
P-value
["0.108", "0.012", "0.885", "0.114", "0.886"]
Initial conclusion.
["Reject the null hypothesis", "Reject the alternative hypothesis", "Fail to reject the null hypothesis", "Fail to reject the alternative hypothesis"]
Final conclusion.
["At 0.05 level of significance, we do not have sufficient evidence to support the claim that the percentage of people following the diet has increased.", "At 0.50 level of significance, we have sufficient evidence to support the claim that the percentage of people following the diet has increased.", "At 0.50 level of significance, we do not have sufficient evidence to reject the claim that the percentage of people following the diet has increased.", "At 0.50 level of significance, we have sufficient evidence to reject the claim that the percentage of people following the diet has increased."]